How do we determine when there is one or two cases for the law of sines

The video tutorial discusses the concept of having two solutions in trigonometry, focusing on the sine and cosine functions. It explains how to find angles where sine or cosine equals a specific value, using the unit circle and inverse functions. The tutorial highlights the importance of considering both acute and obtuse angles when solving trigonometric equations, especially when using inverse sine. It also covers how to calculate these angles and the implications of having two possible solutions.

What is the angle between 0 and π/2 where cosine equals 1/2?

• π/2

• π/4

• π/3

• π/6

Which angle corresponds to sine of theta equaling 1/2 on the unit circle?

• π/6

• π/3

• π/2

• π/4

What is the other angle, besides π/6, where sine equals 1/2?

• π/2

• 5π/6

• 2π/3

• π

How do you find the obtuse angle when given an acute angle in trigonometry?

• Multiply the acute angle by 2

• Add 90 degrees to the acute angle

• Subtract the acute angle from 180 degrees

• Divide the acute angle by 2

Why is it important to consider both acute and obtuse angles in trigonometric solutions?

• To ensure all possible solutions are considered

• To reduce the number of solutions

• To simplify calculations

• To avoid using inverse functions